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Simplifying 16t2 + -169t + -46 = 0 Reorder the terms: -46 + -169t + 16t2 = 0 Solving -46 + -169t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -2.875 + -10.5625t + t2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + -10.5625t + 2.875 + t2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + -10.5625t + t2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + -10.5625t + t2 = 0 + 2.875 -10.5625t + t2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 -10.5625t + t2 = 2.875 The t term is -10.5625t. Take half its coefficient (-5.28125). Square it (27.89160156) and add it to both sides. Add '27.89160156' to each side of the equation. -10.5625t + 27.89160156 + t2 = 2.875 + 27.89160156 Reorder the terms: 27.89160156 + -10.5625t + t2 = 2.875 + 27.89160156 Combine like terms: 2.875 + 27.89160156 = 30.76660156 27.89160156 + -10.5625t + t2 = 30.76660156 Factor a perfect square on the left side: (t + -5.28125)(t + -5.28125) = 30.76660156 Calculate the square root of the right side: 5.546764963 Break this problem into two subproblems by setting (t + -5.28125) equal to 5.546764963 and -5.546764963.Subproblem 1
t + -5.28125 = 5.546764963 Simplifying t + -5.28125 = 5.546764963 Reorder the terms: -5.28125 + t = 5.546764963 Solving -5.28125 + t = 5.546764963 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.28125' to each side of the equation. -5.28125 + 5.28125 + t = 5.546764963 + 5.28125 Combine like terms: -5.28125 + 5.28125 = 0.00000 0.00000 + t = 5.546764963 + 5.28125 t = 5.546764963 + 5.28125 Combine like terms: 5.546764963 + 5.28125 = 10.828014963 t = 10.828014963 Simplifying t = 10.828014963Subproblem 2
t + -5.28125 = -5.546764963 Simplifying t + -5.28125 = -5.546764963 Reorder the terms: -5.28125 + t = -5.546764963 Solving -5.28125 + t = -5.546764963 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.28125' to each side of the equation. -5.28125 + 5.28125 + t = -5.546764963 + 5.28125 Combine like terms: -5.28125 + 5.28125 = 0.00000 0.00000 + t = -5.546764963 + 5.28125 t = -5.546764963 + 5.28125 Combine like terms: -5.546764963 + 5.28125 = -0.265514963 t = -0.265514963 Simplifying t = -0.265514963Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.828014963, -0.265514963}
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